Publications (58)
Wild automorphisms and compound isotriviality
Jason Bell, Rahim Moosa
Inspired by the model theory of difference fields in characteristic zero, a class of automorphisms of an algebraic variety, here called compound fundamental isotrivial, is introduc…
Invariant rational functions under rational transformations
Jason Bell, Rahim Moosa, Matthew Satriano
Let be an algebraic variety equipped with a dominant rational self-map . A new quantity measuring the interaction of with trivial dynamical systems is intro…
An isomorphism lemma for graded rings
Jason Bell, James J. Zhang
Let and be two connected graded algebras finitely generated in degree one. If is isomorphic to as ungraded algebras, then they are also isomorphic to each other as…
Mahler series with multiplicative coefficient sequences
Jason Bell, Daniel Smertnig
We prove that every Mahler series, over a field of characteristic , with multiplicative coefficients is regular in the sense of Allouche and Shallit. We also obtain an explicit…
Consecutive Power Occurrences in Sturmian Words
Jason Bell, Chris Schulz, Jeffrey Shallit
We show that every Sturmian word has the property that the distance between consecutive ending positions of cubes occurring in the word is always bounded by and this bound is…
Effective versions of two theorems of Rado
Jason Bell, Daryl Funk, Byoung Du Kim +1
Let be a representable matroid on elements. We give bounds, in terms of , on the least positive characteristic and smallest field over which is representable.
A conjecture strengthening the Zariski dense orbit problem for birational maps of dynamical degree one
Jason Bell, Dragos Ghioca
We formulate a strengthening of the Zariski dense orbit conjecture for birational maps of dynamical degree one. So, given a quasiprojective variety defined over an algebraicall…
A Dichotomy for -automatic expansions of Presburger Arithmetic
Jason Bell, Alexi Block Gorman, Chris Schulz
Let and let be a subset of the natural numbers that is -automatic and not eventually periodic. We show that the following dichotomy holds: either all -automatic…
Effective isotrivial Mordell-Lang in positive characteristic
Jason Bell, Dragos Ghioca, Rahim Moosa
The isotrivial Mordell-Lang theorem of Moosa and Scanlon describes the set when is a subvariety of a semiabelian variety over a finite field and $Î…
On the growth of algebras, semigroups, and hereditary languages
Jason Bell, Efim Zelmanov
We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.
-finite multivariate series with arithmetic restrictions on their coefficients
Jason Bell, Daniel Smertnig
A multivariate, formal power series over a field is a Bézivin series if all of its coefficients can be expressed as a sum of at most elements from a finitely generated sub…
The Dixmier-Moeglin equivalence for extensions of scalars and Ore extensions
Jason Bell, Kaiyu Wu, Shelley Wu
An algebra satisfies the Dixmier-Moeglin equivalence if we have the equivalences: $$P~{\rm primitive}\iff P~{\rm rational}\iff P ~{\rm locally~closed~}\qquad~{\rm for}~P\in {\r…
Enumeration of torus-invariant strata with respect to dimension in the big cell of the quantum minuscule Grassmannian of type B_n
Jason Bell, Karel Casteels, Stéphane Launois
The aim of this article is to give explicit formulae for various generating functions, including the generating function of torus-invariant primitive ideals in the big cell of the…
Mahler's and Koksma's classifications in fields of power series
Jason Bell, Yann Bugeaud
Let a prime power and the finite field of elements. We study the analogues of Mahler's and Koksma's classifications of complex numbers for power series in $…
Zariski Cancellation Problem for Noncommutative Algebras
Jason Bell, James J. Zhang
A noncommutative analogue of the Zariski cancellation problem asks whether implies when and are noncommutative algebras. We resolve this affirma…
Filtered deformations of commutative algebras of Krull dimension two
Jason Bell
Let be an algebraically closed field of positive characteristic and let be a finitely generated -algebra with a filtration with the property that the associated graded r…
Enveloping algebras of derivations of commutative and noncommutative algebras
Jason Bell, Lucas Buzaglo
Let be a field of characteristic zero. Motivated by the fundamental question of whether it is possible for the universal enveloping algebra of an infinite-dimensional Lie a…
D-groups and the Dixmier-Moeglin equivalence
Jason Bell, Omar Leon Sanchez, Rahim Moosa
A differential-algebraic geometric analogue of the Dixmier-Moeglin equivalence is articulated, and proven to hold for -groups over the constants. The model theory of differentia…
On the Complexity of the Cogrowth Sequence
Jason Bell, Marni Mishna
Given a finitely generated group with generating set , we study the \emph{cogrowth} sequence, which is the number of words of length over the alphabet that are equal to…
Becker's conjecture on Mahler functions
Jason Bell, Frederic Chyzak, Michael Coons +1
In 1994, Becker conjectured that if is a -regular power series, then there exists a -regular rational function such that satisfies a Mahler-type fun…
Primitive ideals in quantum Schubert cells: dimension of the strata
Jason Bell, Karel Casteels, Stéphane Launois
The aim of this paper is to study the representation theory of quantum Schubert cells. Let $\g$ be a simple complex Lie algebra. To each element of the Weyl group of $\g$,…
A strong Dixmier-Moeglin equivalence for quantum Schubert cells
Jason Bell, Stéphane Launois, Brendan Nolan
Dixmier and Moeglin gave an algebraic condition and a topological condition for recognising the primitive ideals among the prime ideals of the universal enveloping algebra of a fin…
Noncommutative rational Pólya series
Jason Bell, Daniel Smertnig
A (noncommutative) Pólya series over a field is a formal power series whose nonzero coefficients are contained in a finitely generated subgroup of . We show that rat…
Maximal dimensional subalgebras of general Cartan type Lie algebras
Jason Bell, Lucas Buzaglo
Let be a field of characteristic zero and let be the general Cartan type Lie algebra. In this pap…
Invariant hypersurfaces
Jason Bell, Rahim Moosa, Adam Topaz
The following theorem, which includes as very special cases results of Jouanolou and Hrushovski on algebraic -varieties on the one hand, and of Cantat on rational dynamics on th…
When is an automatic set an additive basis?
Jason Bell, Kathryn Hare, Jeffrey Shallit
We characterize those -automatic sets of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In additio…
A height gap theorem for coefficients of Mahler functions
Boris Adamczewski, Jason Bell, Daniel Smertnig
We study the asymptotic growth of coefficients of Mahler power series with algebraic coefficients, as measured by their logarithmic Weil height. We show that there are five differe…
Symmetric Groups and Quotient Complexity of Boolean Operations
Jason Bell, Janusz Brzozowski, Nelma Moreira +1
The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L' are binary regular langu…
Birational maps with transcendental dynamical degree
Jason Bell, Jeffrey Diller, Mattias Jonsson +1
We give examples of birational selfmaps of , whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The pro…
The dynamical Mordell-Lang problem for etale maps
Jason Bell, Dragos Ghioca, Thomas J. Tucker
We prove a dynamical version of the Mordell-Lang conjecture for etale endomorphisms of quasiprojective varieties. We use p-adic methods inspired by the work of Skolem, Mahler, and…
Towards a Polya-Carlson dichotomy for algebraic dynamics
Jason Bell, Richard Miles, Thomas Ward
We present results and background rationale in support of a Polya--Carlson dichotomy between rationality and a natural boundary for the analytic behaviour of dynamical zeta functio…
Enumeration of $\C{H}$-strata in quantum matrices with respect to dimension
Jason Bell, Karel Casteels, Stéphane Launois
We present a combinatorial method to determine the dimension of $\C{H}$-strata in the algebra of quantum matrices $\Oq$ as follows. To a given $\C{H}$-stratum we associ…
Topological invariants for words of linear factor complexity
Jason Bell
Given a finite alphabet and a right-infinite word over the alphabet , we construct a topological space consisting of all right-infinite recurrent words…
Frequencies of subwords in words of linear subword complexity
Jason Bell, Laindon Burnett, Chris Schulz
The paper establishes upper bounds on the number of distinct frequencies of subwords in right‑infinite words with linear subword complexity, and shows that these bounds can be exce…
Cogrowth Series for Free Products of Finite Groups
Jason Bell, Haggai Liu, Marni Mishna
Given a finitely generated group with generating set , we study the cogrowth sequence, which is the number of words of length over the alphabet that are equal to one. Th…
On the Weierstrass Preparation Theorem over General Rings
Jason Bell, Peter Malcolmson, Frank Okoh +1
We study rings over which an analogue of the Weierstrass preparation theorem holds for power series. We show that a commutative ring admits a factorization of every power serie…
Sparse regular subsets of the reals
Jason Bell, Alexi Block Gorman
This paper concerns the expansion of the real ordered additive group by a predicate for a subset of whose base- representations are recognized by a Büchi automaton. In…
Characteristic Points of Recursive Systems
Jason Bell, Stanley Burris, Karen Yeats
Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when w…
F-sets and finite automata
Jason Bell, Rahim Moosa
The classical notion of a k-automatic subset of the natural numbers is here extended to that of an F-automatic subset of an arbitrary finitely generated abelian group equipped…
Leavitt path algebras satisfying a polynomial identity
Jason Bell, T. H. Lenagan, Kulumani M. Rangaswamy
Leavitt path algebras L of an arbitrary graph E over a field K satisfying a polynomial identity are completely characterized both in graph-theoretic and algebraic terms. When E is…
Spectra and Systems of Equations
Jason Bell, Stanley Burris, Karen Yeats
In a previous work we introduced an elementary method to analyze the periodicity of a generating function defined by a single equation y=G(x,y). This was based on deriving a single…
Dynamical Uniform Bounds for Fibers and a Gap Conjecture
Jason Bell, Dragos Ghioca, Matthew Satriano
We prove a uniform version of the Dynamical Mordell-Lang Conjecture for étale maps; also, we obtain a gap result for the growth rate of heights of points in an orbit along an arbi…
A differential analogue of the wild automorphism conjecture
Jason Bell, Colin Ingalls, Rahim Moosa +1
A differential analogue of the conjecture of Reichstein, Rogalski, and Zhang in algebraic dynamics is here established: if is a projective variety over an algebraically closed…
Duality of Lattices Associated to Left and Right Quotients
Jason Bell, Daniel Smertnig, Hellis Tamm
We associate lattices to the sets of unions and intersections of left and right quotients of a regular language. For both unions and intersections, we show that the lattices we pro…
Automatic Sequences of Rank Two
Jason Bell, Jeffrey Shallit
Given a right-infinite word over a finite alphabet , the rank of is the size of the smallest set of words over such that can be realized as an in…
Monadic Second-Order Classes of Forests with a Monadic Second-Order 0-1 Law
Jason Bell, Stanley Burris, Karen Yeats
Let $\cT$ be a monadic-second order class of finite trees, and let $\bT(x)$ be its (ordinary) generating function, with radius of convergence . If then $\cT$ has an e…
A fusion variant of the classical and dynamical Mordell-Lang conjectures in positive characteristic
Jason Bell, Dragos Ghioca
We study an open question at the interplay between the classical and the dynamical Mordell-Lang conjectures in positive characteristic. Let be an algebraically closed field of…
Additive Number Theory via Approximation by Regular Languages
Jason Bell, Thomas Finn Lidbetter, Jeffrey Shallit
We prove some new theorems in additive number theory, using novel techniques from automata theory and formal languages. As an example of our method, we prove that every natural num…
Power Series Approximations to Fekete Polynomials
Jason Bell, Igor E. Shparlinski
We study how well Fekete polynomials with the coefficients given by Legendre symbols modulo a prime…
Promoting circular-orderability to left-orderability
Jason Bell, Adam Clay, Tyrone Ghaswala
Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A…
Stably Just Infinite Rings
Jason Bell, John Farina, Cayley Pendergrass-Rice
We study just infinite algebras which remain so upon extension of scalars by arbitrary field extensions. Such rings are called stably just infinite. We show that just infinite ring…
The Dixmier-Moeglin equivalence, Morita equivalence, and homeomorphism of spectra
Jason Bell, Xingting Wang, Daniel Yee
Let be a field and let be a left noetherian -algebra. The algebra satisfies the Dixmier-Moeglin equivalence if the annihilators of irreducible representations are pr…
Diophantine approximation of Mahler numbers
Jason Bell, Yann Bugeaud, Michael Coons
Suppose that is a Mahler function and that is in the radius of convergence of . In this paper, we consider the approximation of by alg…
Quantitative estimates for the size of an intersection of sparse automatic sets
Seda Albayrak, Jason Bell
A theorem of Cobham says that if and are two multiplicatively independent natural numbers then a subset of the natural numbers that is both - and -automatic is…
Rational self-maps with a regular iterate on a semiabelian variety
Jason Bell, Dragos Ghioca, Zinovy Reichstein
Let be a semiabelian variety defined over an algebraically closed field of characteristic . Let be a dominant rational self-map. Assume tha…
Bounded step functions and factorial ratio sequences
Jason Bell, Jonathan Bober
We study certain step functions whose nonnegativity is related to the integrality of sequences of ratios of factorial products. In particular, we obtain a lower bound for the mean…
On prime non-primitive von Neumann regular algebras
Gene Abrams, Jason Bell, Kulumani M. Rangaswamy
Let be any directed graph, and any field. We classify those graphs for which the Leavitt path algebra is primitive. As a consequence, we obtain classes of exam…
Poisson algebras via model theory and differential-algebraic geometry
Jason Bell, Stéphane Launois, Omar León Sánchez +1
Brown and Gordon asked whether the Poisson Dixmier-Moeglin equivalence holds for any complex affine Poisson algebra; that is, whether the sets of Poisson rational ideals, Poisson p…